Input constrained positioning control for a class of Eular-Lagrange systems with discontinuities

In this paper, a nonlinear continuous feedback control scheme is proposed to cope with the positioning control for a class of Eular-Lagrange systems with nonsmooth static friction. Unlike the high gain feedback, the gain of the controller is determined by the range of the positioning error so that it is available for the input saturation. The results also show that all the trajectories will converge to an invariant set and stay in the set which is exactly analyzed based on Filippov´s differential equation theory. Such invariant set contains the static positioning error and its size can be adjusted to the prespecifled accuracy requirement by choosing the feasible control parameters. Finally, to demonstrate the validity of the proposed approaches, some simulation results will be shown.